Regularization of Networks With Improper Port Functions

This paper first defines regular single port linear networks as those which have all their poles and zeros in the finite complex plane. The definition is then extended to cover linear multiport networks by using poles and zeros of the matrix network function. For regular networks state space representation is especially useful in computation of inverse network function and offers advantages in computations. State space representation of network function, however, considers only what are known as proper functions. Such networks are not regular if there are zeros at infinity which are detected in terms of the state space matrices. This paper considers the problem of regularization of networks by incorporating appropriate resistances in series and parallel at the ports and utilizing the state space models for computations. This paper proves that such a regularization is possible under realistic conditions on networks. Examples of two port networks are used to show the construction. Regularization problem is important in practice since with a small tuning at the ports by connecting resistances in the model, a network model can be regularized which offers computational advantages. It is also shown in the beginning that networks obtained by port interconnection of regular networks result into regular networks.